12.1: Chronology
962 CE Otto I crowned Holy Roman Emperor
987 CE Hugh Capet elected king of France
c. 1000 – 1100 CE Emergence of Western European feudalism
1031 CE Fall of the Cordoba Caliphate
1049 CE Pope Leo IX begins papal efforts at Church reform
1054 CE Schism between the pope and the patriarch of Constantinople
1066 CE Norman Conquest of England
1071 CE Battle of Manzikert annihilates Byzantine field army
1077 CE Henry IV repents to Pope Gregory VII at Canossa
1085 CE Fall of Muslim Toledo to the Christian kingdom of Leon-Castile
1088 – 1231 CE Foundation of Universities of Bologna, Paris, Oxford, and Cambridge
1091 CE Norman conquest of Muslim Sicily complete
1095 CE Council of Clermont, calling of the First Crusade
1099 CE Fall of Jerusalem to Christian Crusaders, establishment of Crusader States
1100 – 1135 CE King Henry I rules England
1118 – 1143 CE Emperor John II rules the Byzantine Empire
1122 CE Concordat of Worms
1125 – 1152 CE Raymond is archbishop of Toledo, begins sponsoring the translation of Muslim and Greek philosophy from Arabic into Latin
1143 – 1180 CE Emperor Manuel Komnenos rules the Byzantine Empire
1154 – 1189 CE King Henry II rules England
1176 CE Frederick Barbarossa defeated by Lombard League at the Battle of Legnano; Manuel Komnenos defeated by Saljuq Turks at the Battle of Myriokephalon
1187 CE Kingdom of Jerusalem defeated by Saladin at the Battle of Hattin, fall of Jerusalem, Pope Gregory VIII issues Audita tremendi, calling the Third Crusade
1189 – 1192 CE The Third Crusade, a rump (remnant of a larger government) Christian Kingdom of Jerusalem is re-established, but Jerusalem remains in Muslim hands
1203 – 1226 CE France’s Capetian kings extend the control of lands directly ruled by the crown
1204 CE Crusaders sack Constantinople, break-up of the Byzantine Empire
1212 CE Almohad Caliphate defeated by Spanish Christian kingdoms at the Battle of Las Navas de Tolosa
1215 CE Magna Carta
1215 – 1250 CE Frederick II is Holy Roman Emperor
1224 – 1274 CE Life of St. Thomas Aquinas
1229 CE A treaty between Frederick II and Egyptian sultan al-Kamil returns Jerusalem to Christian rule
1240 CE Mongol Conquest of Kievan Rus
1241 CE Mongol invasion of Hungary
1244 CE Jerusalem falls to Ayyubid Egypt
1248 – 1254 CE The Seventh Crusade, France’s King Louis IX defeated by Egypt, Egyptian Mamluk coup d’état
1250 – 1273 CE There is no Holy Roman Emperor
1261 CE Restoration of the Byzantine Empire
1291 CE Last Crusader territory in the Levant falls to Mamluk Egypt
c. 1300 CE Genoese sailors begin exploring the Atlantic Ocean
early 1300s CE Genoese sailors are visiting the Canary Islands
1309 CE Beginning of Avignon papacy
1314 – 1326 CE Civil war in the Holy Roman Empire
1315 – 1322 CE The Great Famine
1324 CE Mansa Musa’s hajj
1331 CE Nearly all Byzantine territory in Asia Minor has fallen to the Ottoman Turks
1337 CE The Hundred Years’ War begins
c. 1350 CE Beginning of Italian Renaissance and Humanism
1347 – 1351 CE The Black Death, nearly a third of Europe’s population dies
1356 CE The Holy Roman Empire becomes an elected monarchy
1358 CE French peasant revolt
1378 CE Beginning of Great Schism
1385 CE Lithuania united with Poland, Lithuanian monarch converts to Christianity
1396 CE Ottoman Turks conquer Bulgaria
1397 CE Union of Kalmar unites Sweden, Denmark, and Norway under a single crown
c. 1400 – 1500 CE Renaissance Humanism spreads throughout Europe
1404 CE Castilian effort to conquer the Canaries begins
1415 – 1417 CE Council of Constance resolves the Great Schism
1440 CE Lorenzo Valla shows the Donation of Constantine to be a forgery
mid 1400s CE Iberians are settling the Azores, a plantation economy worked by African slaves begins to flourish in the Canaries and Azores
1453 CE Ottoman conquest of Constantinople, final fall of the Byzantine Empire; End of Hundred Years’ War and English attempts to conquer France
1454 CE Treaty of Lodi brings nearly a half century of peace to Italy
1455 – 1485 CE Wars of the Roses in England
1459 CE Final Ottoman conquest of Serbia
1479 CE Marriage of Queen Isabella of Castile and Ferdinand of Aragon creates a united Spanish monarchy
1492 CE King Ferdinand and Queen Isabella complete the Reconquista with the conquest of Granada, Christopher Columbus, sailing for the Spanish crown, makes landfall in the Western Hemisphere
1494 CE France invades Italy


15.15D: Nongonococcal Urethritis (NGU)
- Recognize the symptoms, causes and treatments for nongonococcal urethritis (NGU)
Nongonococcal urethritis (NGU) is a urethral inflammation that is not caused by Neisseria gonorrhoeae, a classification used by doctors for treatment purposes. The general symptoms are pain on urination, frequent need to urinate and white or cloudy discharge. The most common symptoms unique to men are discharge from the penis, itching, and tenderness. In women, the symptoms include vaginal discharge, abdominal pain. If irregular menstrual bleeding is present it may indicate that the infection has progressed into pelvic inflammatory disease.
Diagnosing NGU is based on the lack of Neisseria gonorrhoeae in laboratory testsin a patient with urethritis. In men, it can be diagnosed with Gram staining of urethral discharge; the same is not true for women, since they may have other Gram negative bacteria that are part of their normal vaginal microflora. There are multiple infectious agents that can cause nongonococcal inflammation of the urethra. The most common bacterial agent is Chlamydia trachomatis (about a quarter to half of all NGU cases), though others include Ureaplasma urealyticum, Haemophilus vaginalis and Mycoplasma genitalium . Viral infections can be caused sometimes by the Herpes simplex virus or adenovirus. Parasites such as Trichomonas vaginalis can cause inflammation too, although rarely. NGU can be caused by reasons different than infection, such as the use of some chemicals or physical injuries. Since many different infectious agents can be causing NGU, the initial treatment should be with a broad spectrum antibiotic. Studies indicate that therapies with doxycycline or azithromycin with tinidazole can be more effective than doxycycline or azithromycin alone. Sexual partners of infected patients should be treated as well. Prompt treatment is critical in both men and women. Women are at risk of developing pelvic inflammatory disease (PID), while in men the infection can progress to epididymitis and cause infertility.
Key Points
- The general symptoms are pain on urination, frequent urination, and white or cloudy discharge.
- It can be caused by many infectious agents, with the most common being chlamydia.
- Since many different infectious agents can be causing NGU, the initial treatment should be with a broad spectrum antibiotic.
Key Terms
- epididymitis : An inflammation of the epididymis, a structure in the testicles where sperm matures.


Chapter 1: Crime, Criminal Justice, and Criminology Last updated Save as PDF Page ID 15866 Alison S. Burke, David Carter, Brian Fedorek, Tiffany Morey, Lore Rutz-Burri, & Shanell Sanchez Southern Oregon University via OpenOregon 1.1: Crime and the Criminal Justice System 1.2: Deviance, Rule Violations, and Criminality 1.3: Social Norms- Folkways, Mores, Taboo, and Laws 1.4: Interactionist View 1.5: Consensus View and Decriminalizing Laws 1.6: Conflict View 1.7: The Three C’s- Cops, Courts, and Corrections 1.8: The Crime Control and Due Process Models 1.9: How Cases Move Through the System 1.10: Media Coverage of Crimes 1.11: Wedding Cake Model of Justice 1.12: Street Crime, Corporate Crime, and White-Collar Crime 1.13: Different Types of Crimes and Offenses 1.14: Victims and Victim Typologies 1.15: Victim Rights and Assistance


7.7: Medical Specialists, Diagnostic Testing, and Procedures Related to the Female Reproductive System
Medical Specialists
Gynecology (gī-nĕ-KOL-ŏ-jē) refers to the study of the female reproductive system. A gynecologist (gīn-ĕ-KOL-ŏ-jĭst) (GYN) is a physician who specializes in the diagnosis and treatment of diseases and disorders of the female reproductive system. Obstetrics (ŏb-STĔT-rĭks) is a specialty regarding pregnancy, labor, and delivery of a baby. An obstetrician (OB) is a physician who specializes in providing medical care through pregnancy, labor, and delivery of a baby. Other subspecialties in women’s health include contraception, reproductive endocrinology, infertility, adolescent gynecology, endoscopy, and gynecological oncology . [1]
To learn more about obstetrics or gynecology, visit the specialty and subspecialty page of the American Board of Obstetrics and Gynecology.
Common Diagnostic Tests and Procedures
Many diagnostic tests and procedures are discussed as they apply to female reproductive system disorders in the “Diseases and Disorders of the Female Reproductive System” section. Common diagnostic tests and procedures used for multiple disorders are described below.
Dilation & Curettage (D&C)
Dilation & curettage (dī-LĀ-shŏn and kūr-ĕ-täj) (D&C) is a procedure performed by a physician in which the opening of the cervix is stretched so that a surgical tool can be inserted into the uterus to scrape away the excess endometrial lining. The removed lining is then biopsied for abnormal tissue. A D&C is performed to determine the cause of abnormal vaginal bleeding, as well as to treat it. [2] See Figure 7.10 [3] for an illustration of a D&C.
Hysterectomy, Oophorectomy, and Salpingectomy
A hysterectomy (his-tĕ-REK-tŏ-mē) is a surgery used to treat a variety of disorders, such as dysfunctional uterine bleeding, fibroids, severe endometriosis, endometrial cancer, and ovarian cancer. See Figure 7.11 [4] for an illustration of different types of hysterectomies. There are several types of hysterectomies [5] :
- Total hysterectomy (tō-tăl his-tĕ-REK-tŏ-mē): Surgery to remove the uterus, including the cervix. If the uterus and cervix are taken out through the vagina, the operation is called a vaginal hysterectomy (vă-jĭ-năl his-tĕ-REK-tŏ-mē). If the uterus and cervix are taken out through a large incision in the abdomen, the operation is called a total abdominal hysterectomy (tō-tăl ăb-DŎM-ĭ-năl his-tĕ-REK-tŏ-mē). If the uterus and cervix are taken out through a small incision in the abdomen using a laparoscope, the operation is called a total laparoscopic hysterectomy (tō-tăl lăp-ăr-ŏ-SKŌP-ĭk his-tĕ-REK-tŏ-mē). A subtotal hysterectomy (sŭb-tō-tăl his-tĕ-REK-tŏ-mē) removes part of the uterus but leaves the cervix intact.
- Radical hysterectomy (răd-ĭ-kăl his-tĕ-REK-tŏ-mē): Surgery to remove the uterus, cervix, and part of the vagina. The ovaries, Fallopian tubes, or nearby lymph nodes may also be removed during this procedure, referred to as a total hysterectomy/bilateral salpingectomy oophorectomy (tō-tăl his-tĕ-REK-tŏ-mē / bī-LĂT-ĕr-ăl săl-pĭn-JEK-tŏ-mē ō-ŏ-fŏ-REK-tŏ-mē) (TAH/BSO) . An oophorectomy (ō-ŏ-fŏ-REK-tŏ-mē) is the surgical removal of one ovary. A bilateral oophorectomy (bī-LĂT-ĕr-ăl ō-ŏ-fŏ-REK-tŏ-mē) is the removal of both ovaries. A salpingectomy (sal-pĭn-JEK-tŏ-mē) is the removal of a Fallopian tube. A salpingo-oophorectomy (săl-pĭn-jō-ō-ŏf-ō-RĔK-tō-mē) is removal of one Fallopian tube and the associated ovary. Bilateral salpingo-oophorectomy (bī-LĂT-ĕr-ăl săl-pĭng-gō-ō-ŏ-fŏ-REK-tŏ-mē) means removal of both ovaries and Fallopian tubes.
Hysterosalpingogram
A hysterosalpingogram (hĭs-tĕ-RO-săl-pĭnj-ō-gram) is a common imaging procedure performed to assess for potential causes of infertility in women. During the procedure, radiopaque dye is injected into the uterus and fills the uterine cavity, continues into the Fallopian tubes, and eventually reaches fimbriated ends next to the ovaries. Structures are visualized with an X-ray.
Hysteroscopy
A hysteroscopy (his-tĕ-ROS-kŏ-pē) is a procedure to visually examine the uterus for abnormal areas.  It may also have a tool to remove tissue samples, which are examined under a microscope for signs of cancer. [6] See Figure 7.12 [7] for an illustration of hysteroscopy.
 See Figure 7.13 [8] for an image of a women undergoing a mammogram.
Pap Smear
A Papanicolaou smear (păp-ă-NĒ-kă-low smēr) or Pap smear is a diagnostic test that screens for suspicious changes in cells of the cervix. During a Pap smear, a health care provider inserts a speculum (SPEK-yŭ-lŭm) into the vagina to allow visualization of the cervix. Cells are collected from the cervix using sterile swabs and/or cytobrushes and sent to a lab for analysis for abnormal cells or cancer. See Figure 7.14 [9] for an image of a cytobrush used to collect cervical cell samples during a PAP smear.
Transvaginal Ultrasound
A transvaginal ultrasound (trăns-vă-jĭ-năl ŬL-tră-sound) is a procedure used to examine the vagina, uterus, Fallopian tubes, and bladder. An ultrasound transducer (probe) is inserted into the vagina and used to bounce high-energy sound waves (ultrasound) off internal tissues or organs and make echoes. The echoes form a picture of body tissues called a sonogram. See Figure 7.15 [10] for an illustration of the ultrasound transducer placement during a transvaginal ultrasound.
Tubal Ligation
Tubal ligation (TOO-băl lī-GĀ-shŏn) is surgical procedure performed to prevent pregnancy and is also called female sterilization and commonly referred to as “getting your tubes tied.” “Tubal” refers to the Fallopian tubes, and “ligation” means to tie off. During this surgery, both Fallopian tubes are blocked or cut to prevent fertilization of the egg by sperm. The procedure is usually performed in the hospital or in an outpatient surgical clinic. After the procedure, the woman still has a monthly menstrual cycle and menstrual flow. [11]
- American Board of Medical Specialties. (n.d.). American board of obstetrics and gynecology specialties & subspecialties . https://www.abms.org/board/american-board-of-obstetrics-gynecology/ ↵
- Family Doctor. (2023, June 8). Abnormal vaginal bleeding . American Academy of Family Physicians. https://familydoctor.org/condition/abnormal-uterine-bleeding ↵
- “ Dilation_%26_curettage.svg.png ” by Andrew c is licensed under CC BY-SA 3.0 ↵
- “ me_hysterectomy-en.svg ” by Hic et nunc is licensed in the Public Domain. ↵
- National Cancer Institute. (2020, November 13). Endometrial cancer treatment (PDQ) - Patient version. https://www.cancer.gov/types/uterine/patient/endometrial-treatment-pdq#top ↵
- National Cancer Institute. (2023, June 26). Endometrial cancer screening (PDQ) - Patient version. https://www.cancer.gov/types/uterine/patient/endometrial-screening-pdq ↵
- “Hysteroscopy.png” by BruceBlaus is licensed under CC BY-SA 4.0 ↵
- “Woman_receives_mammogram.jpg” by Rhoda Baer and is licensed in the Public Domain. ↵
- “Cytobrush_for_sampling_endocervical_cells.jpg” by Whispyhistory is licensed under CC BY-SA 4.0 ↵
- “Vaginal_ultrasonography_in_OHSS_-_coronal.png” by BruceBlaus CC BY 3.0 ↵
- Johns Hopkins Medicine. (n.d.). Tubal ligation. www.hopkinsmedicine.org/health/treatment-tests-and-therapies/tubal-ligation ↵


4.28: Introduction to the Bookkeeping Process
What you will learn to do: Discuss the bookkeeping process and the overall effects of transactions
Where does the information found on financial statements originate? It comes from the bookkeeping process! In the bookkeeping process, every financial transaction, no matter how large or small, is accounted for and entered in a journal. These journals create a permanent record of the financial transactions of the business and are eventually transferred to the key financial statements you learned about in the previous section. Consequently, the importance of accurate and timely bookkeeping cannot be understated.
If a question arises about information on a financial statement it can be answered by examining the bookkeeping entries made in the company’s chart of accounts and journals. In this section we will examine an expanded version of the accounting equation and learn how to construct bookkeeping journal entries in order to analyze the relationship among the key financial statements.


3.1.1: Atomic Orbitals and Quantum Numbers
Learning Objectives
- Understand the general idea of the quantum mechanical description of electrons in an atom, and that it uses the notion of three-dimensional wave functions, or orbitals, that define the distribution of probability to find an electron in a particular part of space
- List and describe traits of the four quantum numbers that form the basis for completely specifying the state of an electron in an atom
Understanding Quantum Theory of Electrons in Atoms
Video \(\PageIndex{1}\) : A preview of electrons in orbitals.
The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding.
As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n . This number, n , is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure \(\PageIndex{1}\)). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has.
Figure \(\PageIndex{1}\) : Different shells are numbered by principal quantum numbers.
This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom:
\[ \begin{align*} ΔE &=E_\ce{final}−E_\ce{initial} \\[5pt] &=−2.18×10^{−18}\left(\dfrac{1}{n^2_\ce f}−\dfrac{1}{n^2_\ce i}\right)\:\ce J \end{align*} \]
The values n f and n i are the final and initial energy states of the electron.
The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital , which is distinct from an orbit , is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located.
Another quantum number is l , the angular momentum quantum number . It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l , l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell . In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital.
Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n , p orbitals constitute a p subshell (e.g., 3 p if n = 3). The orbitals with l = 2 are called the d orbitals , followed by the f-, g-, and h- orbitals for l = 3, 4, 5, and there are higher values we will not consider.
There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1.
Figure \(\PageIndex{2}\) : The graphs show the probability (y axis) of finding an electron for the 1s, 2s, 3s orbitals as a function of distance from the nucleus.
Video \(\PageIndex{2}\) : Looking into the probability of finding electrons .
Consider the examples in Figure \(\PageIndex{3}\). The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1 s ( n = 1), 2 – 0 – 1 = 1 node for 2 s , and 3 – 0 – 1 = 2 nodes for the 3 s orbitals.
The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found.
Figure \(\PageIndex{3}\) : Shapes of s, p, d, and f orbitals.
If an electron has an angular momentum ( l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number , called m l, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of m l is zero. For p orbitals, l = 1, and m l can be equal to –1, 0, or +1. Generally speaking, m l can be equal to – l , –( l – 1), …, –1, 0, +1, …, ( l – 1), l . The total number of possible orbitals with the same value of l (a subshell) is 2 l + 1. Thus, there is one s -orbital for ml = 0 , there are three p -orbitals for ml = 1 , five d -orbitals for ml = 2 , seven f -orbitals for ml = 3 , and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure \(\PageIndex{3}\).
Figure \(\PageIndex{4}\) : The chart shows the energies of electron orbitals in a multi-electron atom.
Figure \(\PageIndex{4}\) illustrates the energy levels for various orbitals. The number before the orbital name (such as 2 s , 3 p , and so forth) stands for the principal quantum number, n . The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of m l . In the case of a hydrogen atom or a one-electron ion (such as He + , Li 2 + , and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n , are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf , such as 2 p , 3 s ) are still degenerate and have the same energy.
While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number , or m s .
The other three quantum numbers, n , l , and m l , are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x , y , and z ). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates.
The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number \(m_s=\dfrac{1}{2}\). The other is called the β state, with the z component of the spin being negative and \(m_s=−\dfrac{1}{2}\). Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having \(m_s=−\dfrac{1}{2}\) and \(m_s=\dfrac{1}{2}\) are different if an external magnetic field is applied.
Figure \(\PageIndex{5}\) : Electrons with spin values \( ±\ce{1/2}\) in an external magnetic field.
Figure \(\PageIndex{5}\) illustrates this phenomenon.  Its moment is directed up (in the positive direction of the z axis) for the \(\dfrac{1}{2}\) spin quantum number and down (in the negative z direction) for the spin quantum number of \(−\ce{1/2}\). A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with \(m_s=\dfrac{1}{2}\) has a slightly lower energy in an external field in the positive z direction, and an electron with \(m_s=−\dfrac{1}{2}\) has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting.
Video \(\PageIndex{3}\) : The uncertainty of the location of electrons .
The Pauli Exclusion Principle
An electron in an atom is completely described by four quantum numbers: n , l , m l , and m s . The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n , l , and m l ), but only if their spin quantum numbers m s have different values. Since the spin quantum number can only have two values \(\left(±\dfrac{1}{2}\right)\), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly summarized in Table \(\PageIndex{1}\).
| Name | Symbol | Allowed values | Physical meaning |
|---|---|---|---|
| principal quantum number | n | 1, 2, 3, 4, …. | shell, the general region for the value of energy for an electron on the orbital |
| angular momentum or azimuthal quantum number | l | 0 ≤ l ≤ n – 1 | subshell, the shape of the orbital |
| magnetic quantum number | m l | – l ≤ m l ≤ l | orientation of the orbital |
| spin quantum number | m s | \(\dfrac{1}{2},\:−\dfrac{1}{2}\) | direction of the intrinsic quantum “spinning” of the electron |
Example \(\PageIndex{1}\): Working with Shells and Subshells
Indicate the number of subshells, the number of orbitals in each subshell, and the values of l and m l for the orbitals in the n = 4 shell of an atom.
Solution
For n = 4, l can have values of 0, 1, 2, and 3. Thus, s , p , d , and f subshells are found in the n = 4 shell of an atom. For l = 0 (the s subshell), m l can only be 0. Thus, there is only one 4 s orbital. For l = 1 ( p -type orbitals), m can have values of –1, 0, +1, so we find three 4 p orbitals. For l = 2 ( d -type orbitals), m l can have values of –2, –1, 0, +1, +2, so we have five 4 d orbitals. When l = 3 ( f -type orbitals), m l can have values of –3, –2, –1, 0, +1, +2, +3, and we can have seven 4 f orbitals. Thus, we find a total of 16 orbitals in the n = 4 shell of an atom.
Exercise \(\PageIndex{1}\)
Identify the subshell in which electrons with the following quantum numbers are found:
- n = 3, l = 1;
- n = 5, l = 3;
- n = 2, l = 0.
- Answer a
-
3 p
- Answer b
-
5 f
- Answer c
-
2s
Example \(\PageIndex{2}\): Maximum Number of Electrons
Calculate the maximum number of electrons that can occupy a shell with (a) n = 2, (b) n = 5, and (c) n as a variable. Note you are only looking at the orbitals with the specified n value, not those at lower energies.
Solution
(a) When n = 2, there are four orbitals (a single 2 s orbital, and three orbitals labeled 2 p ). These four orbitals can contain eight electrons.
(b) When n = 5, there are five subshells of orbitals that we need to sum:
&\phantom{+}\textrm{1 orbital labeled }5s\\
&\phantom{+}\textrm{3 orbitals labeled }5p\\
&\phantom{+}\textrm{5 orbitals labeled }5d\\
&\phantom{+}\textrm{7 orbitals labeled }5f\\
&\underline{+\textrm{9 orbitals labeled }5g}\\
&\,\textrm{25 orbitals total}
\end{align*}\)
Again, each orbital holds two electrons, so 50 electrons can fit in this shell.
(c) The number of orbitals in any shell n will equal n 2 . There can be up to two electrons in each orbital, so the maximum number of electrons will be 2 × n 2
Exercise \(\PageIndex{2}\)
If a shell contains a maximum of 32 electrons, what is the principal quantum number, n ?
- Answer
-
n = 4
Example \(\PageIndex{3}\): Working with Quantum Numbers
Complete the following table for atomic orbitals:
| Orbital | n | l | m l degeneracy | Radial nodes (no.) |
|---|---|---|---|---|
| 4 f | ||||
| 4 | 1 | |||
| 7 | 7 | 3 | ||
| 5 d |
Solution
The table can be completed using the following rules:
- The orbital designation is nl , where l = 0, 1, 2, 3, 4, 5, … is mapped to the letter sequence s, p , d , f , g , h , …,
- The m l degeneracy is the number of orbitals within an l subshell, and so is 2 l + 1 (there is one s orbital, three p orbitals, five d orbitals, seven f orbitals, and so forth).
- The number of radial nodes is equal to n – l – 1.
| Orbital | n | l | m l degeneracy | Radial nodes (no.) |
|---|---|---|---|---|
| 4 f | 4 | 3 | 7 | 0 |
| 4 p | 4 | 1 | 3 | 2 |
| 7 f | 7 | 3 | 7 | 3 |
| 5 d | 5 | 2 | 5 | 2 |
Exercise \(\PageIndex{3}\)
How many orbitals have l = 2 and n = 3?
- Answer
-
The five degenerate 3 d orbitals
Summary
Video \(\PageIndex{4}\) : An overview of orbitals.
An atomic orbital is characterized by three quantum numbers. The principal quantum number, n , can be any positive integer. The general region for value of energy of the orbital and the average distance of an electron from the nucleus are related to n . Orbitals having the same value of n are said to be in the same shell. The angular momentum quantum number, l , can have any integer value from 0 to n – 1. This quantum number describes the shape or type of the orbital. Orbitals with the same principal quantum number and the same l value belong to the same subshell. The magnetic quantum number, m l , with 2 l + 1 values ranging from – l to + l , describes the orientation of the orbital in space. In addition, each electron has a spin quantum number, m s , that can be equal to \(±\dfrac{1}{2}\). No two electrons in the same atom can have the same set of values for all the four quantum numbers.
Glossary
- angular momentum quantum number ( l )
- quantum number distinguishing the different shapes of orbitals; it is also a measure of the orbital angular momentum
- wavefunction ( ψ )
- mathematical description of an atomic orbital that describes the shape of the orbital; it can be used to calculate the probability of finding the electron at any given location in the orbital, as well as dynamical variables such as the energy and the angular momentum
- subshell
- set of orbitals in an atom with the same values of n and l
- spin quantum number ( m s )
- number specifying the electron spin direction, either \(+\dfrac{1}{2}\) or \(−\dfrac{1}{2}\)
- shell
- set of orbitals with the same principal quantum number, n
- s orbital
- spherical region of space with high electron density, describes orbitals with l = 0. An electron in this orbital is called an s electron
- quantum mechanics
- field of study that includes quantization of energy, wave-particle duality, and the Heisenberg uncertainty principle to describe matter
- principal quantum number ( n )
- quantum number specifying the shell an electron occupies in an atom
- Pauli exclusion principle
- specifies that no two electrons in an atom can have the same value for all four quantum numbers
- p orbital
- dumbbell-shaped region of space with high electron density, describes orbitals with l = 1. An electron in this orbital is called a p electron
- magnetic quantum number ( m l )
- quantum number signifying the orientation of an atomic orbital around the nucleus; orbitals having different values of m l but the same subshell value of l have the same energy (are degenerate), but this degeneracy can be removed by application of an external magnetic field
- Heisenberg uncertainty principle
- rule stating that it is impossible to exactly determine both certain conjugate dynamical properties such as the momentum and the position of a particle at the same time. The uncertainty principle is a consequence of quantum particles exhibiting wave–particle duality
- f orbital
- multilobed region of space with high electron density, describes orbitals with l = 3. An electron in this orbital is called an f electron
- electron density
- a measure of the probability of locating an electron in a particular region of space, it is equal to the squared absolute value of the wave function ψ
- d orbital
- region of space with high electron density that is either four lobed or contains a dumbbell and torus shape; describes orbitals with l = 2. An electron in this orbital is called a d electron
- atomic orbital
- mathematical function that describes the behavior of an electron in an atom (also called the wavefunction), it can be used to find the probability of locating an electron in a specific region around the nucleus, as well as other dynamical variables
Contributors and Attributions
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).
- Adelaide Clark, Oregon Institute of Technology
- Crash Course Physics: Crash Course is a division of Complexly and videos are free to stream for educational purposes.
- Crash Course Chemistry: Crash Course is a division of Complexly and videos are free to stream for educational purposes.
- TED-Ed’s commitment to creating lessons worth sharing is an extension of TED’s mission of spreading great ideas. Within TED-Ed’s growing library of TED-Ed animations, you will find carefully curated educational videos, many of which represent collaborations between talented educators and animators nominated through the TED-Ed website.


3.4: Working Conditions
Special Clothing (Uniforms)
Many employees in the restaurant and food service industry are required to wear uniforms when they are at work. If you must wear a uniform or a specific brand of clothing, the employer must provide, clean, and maintain it. For example, many cooks must wear white jackets and hats and checked trousers. Your employer must buy the uniform. You cannot be charged for the uniform or for damages to it. Your employer cannot require you to pay a deposit for the uniform or withhold your wages.
The majority of employees and the employer may agree that employees will clean and maintain the special clothing and be reimbursed by the employer for the expenses incurred. This agreement is binding on all employees in the workplace who are required to wear the special clothing.
If an employer and a majority of the employees have agreed that the employer will reimburse employees for the cost of cleaning and maintaining special clothing, the employer must keep records of the agreement and the amounts paid for two years.
Statutory Holidays
Restaurant and food service workers are often required to work when others are on holiday. Holidays such as Christmas and New Year’s Day are frequently the times that people want to go out for dinner, and so restaurants may be especially busy during these times. These days are known as statutory holidays. In British Columbia, the following days are statutory holidays:
- New Year’s Day (January 1)
- Family Day (third Monday in February)
- Good Friday (changes from year to year)
- Victoria Day (the third Monday in May)
- Canada Day (July 1)
- B.C. Day (the first Monday in August)
- Labour Day (the first Monday in September)
- Thanksgiving Day (the second Monday in October)
- Remembrance Day (November 11)
- Christmas Day (December 25)
Easter Sunday, Easter Monday, and Boxing Day are not statutory holidays, although some employers may provide paid time off on these days.
Eligibility
You are not automatically eligible to statutory holidays with pay as soon as you have begun work. You must have worked for the employer for at least 30 calendar days.
Managers (that is, those whose primary employment duties consist of supervising and directing other employees) or a person employed in an executive capacity are not entitled to statutory holidays. They may, however, have negotiated similar provisions in their terms of employment.
Calculating Statutory Holiday Pay
If you have a regular schedule of hours and if you have worked at least 15 days out of the last 30 calendar days prior to a statutory holiday, you are entitled to a regular day’s pay for the holiday. If you have worked irregular hours on at least 15 out of the last 30 calendar days, you are entitled to an average day’s pay for the holiday. This amount is calculated by dividing the employee’s total wages, excluding overtime, by the number of days worked.
An employee who has worked fewer than 15 days in the 30 calendar days before the holiday is entitled to pro-rated holiday pay. This amount is calculated by dividing the total pay during the period, excluding overtime, by 15.
For example, Meilin, Ming, and Steve are all employed in a local restaurant. Meilin is a regular employee who worked 20 eight-hour shifts over the 30 days prior to the holiday. She is entitled to eight hours of pay on the statutory holiday. Ming started work just two weeks before the holiday. He is not entitled to be paid for the holiday. Steve is a part-time employee who has been working for the restaurant for six months. He worked only 12 shifts during the 30 calendar days before the holiday and earned $480 during that time. He is entitled to a payment of $480 ÷ 15 = $32.00 for the holiday.
But what would happen to an employee who is on paid vacation leave prior to the holiday? According to the Act, the vacation days and vacation pay are counted as days worked and wages earned when calculating statutory holiday pay.
Working on a Statutory Holiday
Cooks and other workers in the restaurant and food service industry often work on statutory holidays. It is no surprise that the legislation covers this situation. If you work on the holiday, you must be paid time-and-a-half for the first 12 hours you work and double time for hours beyond 12. You must also be given an alternate day off with pay. If you have a time bank, you may credit the wages for the alternate day.
The employer must schedule the alternate day of paid leave on the earliest of the following:
- Before the employee’s annual vacation
- Before the date the employment terminates
- Within six months of the statutory holiday if the wages were credited to a time bank
Employees not eligible for the statutory holiday who work on the holiday may be paid as if it were a regular workday. They are not entitled to the day off. If a statutory holiday falls on a day on which you are not normally scheduled for work, you are entitled to an alternate day off with pay. This day must be scheduled as if you had worked on the statutory holiday.
By agreement between the employer and a majority of affected workers, the employer may substitute another day off for a statutory holiday. For example, the employer and staff may agree to substitute Easter Monday for Good Friday. The Act and the Regulations will then apply to Easter Monday as if it were a statutory holiday. If the employer and a majority of employees have agreed to substitute another day for a statutory holiday, the employer must keep records of this agreement for two years.
Leave from work
Employers must grant employees periods of unpaid absence from work for the following:
- Pregnancy leave
- Parental leave
- Family responsibility leave
- Bereavement leave
- Jury duty
Employees are eligible for unpaid leave as soon as they have commenced employment. Employers are not required to give employees paid leave for illness. If sick leave is paid or allowed, it may not be deducted at a later date from any other entitlement to a paid holiday, vacation pay, or other wages. Employees who are ill for extended periods of time may be eligible for Employment Insurance.
Pregnancy leave
A pregnant employee is entitled to up to 17 consecutive weeks of unpaid pregnancy leave. This leave may start no earlier than 11 weeks before the expected birth date and end no earlier than six weeks after the birth period unless the employee requests a shorter period. If the pregnancy leave is first requested after the birth of a child or after termination of the pregnancy, an employee is entitled to up to six consecutive weeks of leave beginning on the date of birth or termination date.
An initial period of leave may be extended up to six weeks if an employee is unable to return to work for reasons relating to the birth or the termination of the pregnancy.
The employee must apply, in writing, to take a pregnancy leave. The request must be made at least four weeks before the proposed start date. If the employee wishes to return to work earlier than six weeks from the birth date, she must make the request to return at least one week before the proposed start date. The employer may require the employee to provide a doctor’s certificate in support of a request for leave or for a leave extension. Pregnancy and parental leaves are unpaid leaves, but you may be eligible for maternity and parental benefits under the Canada Employment Insurance Program.
Parental leave
Parental leave is available to a birth mother, a birth father, or an adopting parent.
A birth mother is entitled to up to 35 consecutive weeks of unpaid parental leave in addition to the pregnancy leave she has taken. If she has not taken pregnancy leave, the birth mother is eligible for up to 37 consecutive weeks of unpaid parental leave. A birth mother will commence her parental leave immediately after her pregnancy leave ends unless the employee and employer agree otherwise. A birth mother who is entitled to up to 37 weeks of leave will commence the leave after the child’s birth and within 52 weeks of that event. A birth father is entitled to up to 37 consecutive weeks of unpaid leave beginning after the child’s birth and within 52 weeks of the event. An adopting parent is entitled to up to 37 consecutive weeks of unpaid parental leave beginning within 52 weeks after the child is placed with the parent.
Parents must apply in writing for parental leave at least four weeks prior to the proposed start date of the leave. An employer may require an employee to provide a doctor’s certificate or other evidence that the employee is entitled to the leave or leave extension.
As soon as parental leave ends, the employer must place the employee into the position previously held by the employee or in a comparable position.
Family responsibility leave
An employee is entitled to up to five days of unpaid leave per employment year to meet responsibilities related to the care, health, or education of any member of the employee’s immediate family. Under the legislation, immediate family means the spouse, child, parent, guardian, sibling, grandchild, or grandparent of an employee, and any person who lives with the employee as a member of the employee’s family.
For example, Bart lives in a household with his mother-in-law and children. Bart’s mother-in-law has broken her hip and requires surgery. Bart is entitled to family responsibility leave in order to care for her. Susan and Pat live together. In the event of an illness, Pat would be entitled to leave to care for her partner.
Bereavement leave
Employees are entitled to up to three days of unpaid leave on the death of a member of the employee’s immediate family.
Jury duty
Jury duty is considered a responsibility of citizenship for all citizens of Canada. Individuals may be excused from jury duty only if a judge feels that the duty would impose undue hardship on the individual and his or her family. An employee who is required to attend court as a juror is considered to be on unpaid leave for the period of the jury duty.
Employment considered continuous
During the time an employee is on unpaid leave, employment is considered continuous for the purposes of calculating annual vacation and termination entitlements, as well as for pension, medical, or other plans of benefit for the employee. An employer must continue to make payments to any such plans unless the employee chooses not to continue with his or her share of the cost of the plan. The employee is also entitled to all increases in wages or benefits which he or she would have received if not on leave.
Conditions of employment
An employer cannot terminate an employee on leave or jury duty or change a condition of employment without the employee’s written consent. As soon as the leave or jury duty ends, the worker must be returned to his or her former position or a comparable one.
Consideration for the employer
Whenever possible, it is only considerate to inform the employer as soon as possible when leave is required. For example, if you have been called for jury duty, you will have been given a date on which to appear at the courthouse. Let your employer know so that alternate arrangements can be made for your replacement. Of course, there are times, such as the sudden illness or death of a family member, when it is not possible to notify your supervisor ahead of time. However, you should do your best to call as soon as you can and give the supervisor an idea of when you will return.
Annual vacation
After you have been employed for 12 consecutive months, you are entitled to two weeks of paid vacation. After five consecutive years of employment with the same employer, you are entitled to three weeks. During the first 12 months of employment, the Employment Standards Act does not require that you be granted an annual vacation. However, the terms of employment or a collective agreement may provide additional vacation benefits.
An employer must schedule an employee’s vacation in periods of one or more weeks, unless the employee requests otherwise. Vacation must be taken within 12 months of earning it. The employer may use a common date for calculating the annual vacation entitlement of all employees as long as no employee’s right to an annual vacation or vacation pay is reduced.
If the company is sold, leased, or transferred during the year, your period of consecutive employment is not interrupted. For example, the restaurant in which Sally works was purchased by another chain and subsequently closed, but she was transferred to another location operated by the purchasing company without any loss of employment. Her period of employment was not interrupted, even though her pay cheques were now issued by another company.
Vacation Pay
In the first four years of consecutive employment, the employer must pay vacation pay of at least 4% of all earning paid to the employee in the preceding year. In the fifth and subsequent years of employment, the employer must pay vacation pay of at least 6% of all wages paid in the preceding year. Any vacation pay received by an employee is counted as part of the total wages paid in a particular year. Employees who have worked five calendar days or less are not eligible for vacation pay.
If a statutory holiday falls during the period in which the employee is on annual vacation leave, the employee must be given an additional day of vacation leave in lieu of the statutory holiday. For example, Raj is on holiday for two weeks at the beginning of September. This period includes one statutory holiday, Labour Day. He must be given an additional day of holiday at another time or may have a day in lieu of the statutory holiday added to the beginning or end of his vacation period.
Vacation pay is payable at least seven days before the start of the annual vacation, or on regular pay days as agreed to by the employer and employee, or by a collective agreement.
An employer cannot reduce annual vacation or vacation pay because the worker was paid a bonus or sick pay, or was previously given a vacation more than the minimum. However, these vacation entitlements may be reduced if an employee took annual vacation in advance at the employee’s written request.
If your employment is terminated before you have taken your annual vacation or if you quit your job, you are entitled to be paid any vacation pay that has accrued since you started work or last took annual vacation. This payment must be made within 48 hours if your employment was terminated or within six days if you quit your job.
Hours of Work
The employer must post notices saying when work starts and ends, when each shift starts and ends, and when meal breaks will occur (Figure 6). For example, a restaurant may have a morning shift that begins at 6:00 a.m. and ends at 2:00 pm. The workers on that shift get a meal break at 9:30 am. These notices must be posted where they can be read by all employees.
Shift changes
In the food service industry, work schedules are often developed with different start and end times for different employees. In addition, the industry is sometimes subject to changes in the demand for service. A restaurant may be unexpectedly busy on a day that is normally quiet. Employees must be given 24 hours’ notice of a change in shift unless the employee is paid overtime for the time worked or the shift is extended before it ends. If the employee has not been given the required notice, he or she cannot be penalized for failing to show up for work.
This means, for example, that if a restaurant is extremely busy, you may ask Genevieve, the bus person, to stay for an additional two hours an hour before she finishes her five-hour shift without paying overtime. This assumes that she is not entitled to overtime because of the number of hours she has worked in this pay period or because of a collective agreement.
Meal breaks
After working for five hours in a row, employees are entitled to a half-hour meal break. An employee who is required to work or be available for work during a meal break must be paid for the break. In the food service industry, breaks are often taken between a rush of customers, and a cook may have to cut a break short to cope with new orders. If the cook must be prepared to cut a break short, she or he must be paid for the break, even if on that day the break was not interrupted.
Coffee breaks are not required by the legislation. Employers have the discretion to give coffee breaks. Some collective agreements may specify coffee breaks as part of the conditions of employment.
Split shifts
A split shift is a work pattern in which an employee works for several hours, is off for several hours, and then is asked to work for another period during the same day. When an employee is scheduled for a split shift, the employee must finish for the day within 12 hours of the time he or she began the shift. For example, you could not schedule a dishwasher to come in from 7:00 a.m. to 11:00 a.m., and then again from 6:00 p.m. to 10:00 p.m. on the same day. You could, however, have the dishwasher work from 11:00 to 3:00 and then again from 6:00 to 10:00 for the same number of total hours.
Excessive hours
Employers must not require or allow an employee to work excessive hours or hours harmful to the employee’s health or safety. At present, what constitutes excessive hours is not specified in the Act or Regulations .
Minimum daily pay
An employee who starts work must be paid for at least two hours, even if the employee works for a fewer number of hours. If the work is suspended for reasons beyond the employer’s control, for example, a power failure due to a storm that cannot be repaired that evening, the employee must be paid for two hours of work or the actual number of hours worked, whichever is greater.
For example, a restaurant is experiencing a very slow night. Normally, this evening would be busy, but perhaps because of the cooler temperatures, people are staying home. You could be sent home early, but your employer would have to pay you for at least two hours.
If an employee has reported for work but has not actually started work, he or she must be paid for at least two hours if there is insufficient work. The exception is if the employee is unfit for work or does not comply with the health and safety provisions of WorkSafeBC regulations. For example, an employee who shows up for work under the influence of alcohol could be sent home without being paid for a minimum of two hours.
Hours Free from Work
Employees must have at least 32 hours in a row free from work each week. If an employee works during this period, the employer must pay one-and-a-half times the regular wage for the hours worked. An employee is also entitled to have eight hours off between shifts unless the employee is required to work because of an emergency.
For example, a cook has been working from 5:00 p.m. to midnight on a Thursday evening. The cook is due for a break of at least 32 hours. The earliest he or she could be scheduled after the break would be at 8:00 a.m. on Saturday morning.
Overtime
The standard work day is eight hours and the standard work week is 40 hours. If employees work over eight hours in a day or over 40 hours in a week, they must be paid overtime. The exception is when the employer has implemented a flexible work schedule or if the Employment Standards Branch has granted a variance. Depending on the schedule worked, an employee could be eligible for overtime on the basis of the hours worked in a day, the hours worked in the week, or both. Daily and weekly overtime are calculated separately.
An employer can require you to work overtime as long as the applicable overtime wage rates are paid. In addition, the hours worked should not be excessive or detrimental to the employee’s health or safety. Excessive is not defined in the Act or Regulations . In the case of a dispute, the Director of the Employment Standards Branch would be required to adjudicate what excessive hours are.
Daily and weekly overtime
After working eight hours in a day, an employee is entitled to time and a half for the next four hours worked, and double time for all hours worked in excess of 12 hours.
After working 40 hours in a week, employees must be paid time and a half for the next eight hours and double time for hours in excess of 48. In calculating the total hours worked for weekly overtime purposes, only the first eight hours worked on each day are counted.
For example, if Mohinder works 10 hours on Sunday, seven hours on Monday, seven hours on Tuesday, eight hours on Thursday, and eight hours on Friday, he has worked a total of 40 hours over the five days. He was also asked to work on Saturday. His employer gave the required 24 hours’ notice. For the purposes of calculating weekly overtime, only the first eight hours of each day would be counted. The first eight hours on Sunday would be counted as would all of his shifts on the Tuesday through Friday for a total of 38 hours. He would be paid regular time for the first two hours he worked on Saturday, and after that would receive time and a half. Of course, he would also receive one and a half time (daily overtime) for the extra hours he worked on the Sunday.
In a week with a statutory holiday, an employee who qualifies for the holiday must be paid weekly overtime and time and a half after 32 hours and double time after 40 hours. Any time worked by the employee on the holiday is not included in calculating weekly overtime.
Banking overtime
Employees may request in writing that the employer establish a time bank and credit the employee’s overtime wages to the bank instead of paying the wages as they are earned. An employee may at any time request the employer to pay out all or part of the wages in the time bank. The employee may also request time off with pay for some mutually agreed period.
An employee may request that the time bank be closed. If the employee quits, is laid off, is fired, or has requested that the time bank be closed, the employer must pay the full outstanding balance to the worker. All banked wages must be paid out within six months of being earned. If a number of employees have time banks, then the employer can set a common date for paying out the banked time as long as all wages are paid within six months of being earned.
Training
If the employer requires the employee to attend a training or orientation session or attend a meeting outside of the employee’s normal working hours, the employee must be paid. The employee may be eligible for overtime, minimum daily pay, or other provisions under the Act . For example, George was required by his employer to attend a one-hour training session on a day he was not scheduled for work. He must be paid for at least two hours (minimum daily pay). If he had already worked 40 hours in that week, then he must also be paid overtime.
Flexible Work Schedules
Flexible work schedules are schedules in which the employees may work more than eight hours on a given day or 40 hours in a given week without being paid overtime. For example, an employer may agree to a four-day work week in which employees work 10 hours each day.
This may be beneficial to both employers and employees. Employers may find that scheduling for their opening hours is easier and requires less overtime when a flexible work schedule is used. Employees may enjoy the extra day on which they do not work. Another example is the employer whose employees work nine 8.75 hours days in a two-week period. In one week, employees may work five days for a total of 43.75 hours, but the following week they work only four days (35 hours). The average number of hours per week over two weeks is just over 39 hours.
Workers not covered by a collective agreement
If the workers are not unionized, flexible work schedules must:
- Fit the models permitted by the Regulation
- Run at least 26 weeks
- Be approved by at least 65% of the affected employees
- Be submitted to the Employment Standards Branch within seven days of approval by the employees
Workers must be given an opportunity to hear about the proposed schedule and think about its implications. An information bulletin outlining the proposed schedule must be posted for at least 10 days prior to the approval by employees. Employers may cancel a flexible work schedule at any time. The Branch can also cancel a schedule if it is satisfied that the employer did not follow the procedures in the Regulation or that the employer forced any employees to approve the schedule. The Branch will act only after receiving a written complaint from one of the employees affected by the schedule. A schedule expires two years after it is approved, but may be renewed with the approval of 65% of the affected employees.
Where workers on a flexible work schedule work more than an average of eight hours a day or 40 hours a week over the shift cycle, overtime wages must be paid. For example, James normally works four 10-hour shifts per week. If on one of those days he is asked to work an additional three hours, he would be entitled to overtime for those hours. If he is brought in on a day he does not normally work, he would also be entitled to overtime wages.
Unionized employees
Where workers are covered by a collective agreement, the flexible work schedule must:
- Run for at least 26 weeks
- Consist of a shift cycle of days at work and days off work that repeats over a period of up to eight consecutive weeks
- Allow each affected employee to work an average of at least 35 hours and not more than 40 hours during the shift cycle at the regular rate of pay
- Be approved by the trade union representing the workers affected.
Overtime wages, as required by the collective agreement, must be paid when the employee works more than an average of eight hours per day or 40 hours a week over the shift cycle.
If your employer has a flexible work schedule, records relating to its approval must be kept for seven years.
Averaging Agreements
As opposed to a flexible or alternative work schedule, which is permanent, an employer may decide to use an averaging agreement for a short period of time when the employee’s schedule might vary. This could be used in the case of a business trip or an event that might require a few longer days one week and allowing extra time off the following week. As long as the total number of hours per week do not average more than 40, no overtime pay is required unless the employee works more than 12 hours in any one day, in which case regular daily overtime rates (double the usual hourly rate) will apply.
Averaging agreements can be for a term of one to four weeks and must be agreed to and signed by both the employee and employer in advance. They also must be accompanied by a schedule of anticipated hours over the entire period of the agreement and state the start and end dates of the agreement.
Layoff
Notice is also not required if an employee is laid off temporarily. A temporary layoff becomes a termination when a layoff exceeds 13 weeks in any period of 20 weeks, or a recall period covered by a collective agreement has been exceeded by more than 24 hours. A week of layoff is one in which the employee earns less than 50% of the regular weekly wages averaged over the previous eight weeks. If a temporary layoff becomes a termination, then the date of layoff becomes the termination date. The employee is entitled to the compensation for termination. Any layoff other than a temporary layoff is considered a termination.
Notice of termination
An employee who is terminated by an employer is eligible for compensation based on the length of her or his employment with the employer. The amount of compensation is as follows:
- After three months’ consecutive employment, one week’s pay
- After one year, two weeks’ pay
- After three years, three weeks’ pay, plus one week for each additional year of employment up to a maximum of eight years
If an employer substantially alters a condition of employment, the Employment Standards Branch may determine that the employee’s employment has been terminated. If the Branch decides that the employment was terminated, the employee is eligible for compensation.
A week’s pay is calculated by totalling the employee’s wages excluding overtime, earned in the last eight weeks of which the employee worked normal hours, and dividing by eight. As with calculations of annual vacation, the sale, transfer, or lease of the business does not interrupt an employee’s period of continuous employment.
Termination pay is required even if the employee has obtained other employment.
Compensation is not required if the employee is given advance written notice of the termination equal in number of weeks to the number of week’s pay for which the employee is eligible. An employee cannot be on vacation, leave, strike, or lockout, or be unavailable for work for medical reasons during the notice period. If employment continues after the notice period has ended, the notice is of no effect. Once notice has been given, the employer may not alter any condition of employment, including the wage rate, without the employee’s written consent.
An employer may give an employee a combination of notice and compensation equal to the number of weeks’ pay for which the employee is eligible.
For example, a hotel has just been sold to a developer who will turn the building into condominium units. The hotel owner employs 37 people including a number of cooks. The cooks have worked for the hotel for varying periods of time, ranging from five months to seven years. The owner has the option of giving the cooks notice of termination seven weeks before the closure of the hotel. One of the cooks was on three weeks’ holiday when the deal was signed. This employee, who had five years of continuous employment, could not be given notice. When the employee returned to work, four weeks before the closure, he was given four weeks’ notice and 1 week’s pay to compensate for the termination of employment. Alternatively, the employer could have provided compensation in lieu of notice for all of the employees.
Some examples of the appropriate compensation are as follows:
- Steve, five months of consecutive employment received one week’s pay
- Geoff, 13 months of consecutive employment received two weeks’ pay
- Anya, three years of consecutive employment received three weeks’ pay
- Lupe, seven years of consecutive employment received seven weeks’ pay
Notice of termination or pay compensation is not required if:
- The employee quits or retires
- The employee was dismissed for just cause
- The employee works on an on-call basis doing temporary assignments that may be accepted or rejected
- The employee was employed for a definite term provided that the employment was not extended for at least three months after the term was ended
- The employee was hired for specific work to be completed in 12 months or less
- Events or circumstances beyond the employer’s control (except bankruptcy, receivership, or insolvency) made it impossible to perform the work
- The employee refused reasonable alternative employment
Some employers in specific industries (e.g., construction) or those hiring persons in some occupations (e.g., teacher) may not be required to give notice or pay compensation on termination of employment.
An employer operating a seasonal resort would not have to give notice or pay compensation at the close of the regular season. The employees would be hired for a specific term ending on the closure date of the resort. If a fire destroyed the resort mid-way through the season, the employer would not be required to give notice or pay compensation because the fire is an event beyond the employer’s control. If, on the other hand, the resort was bankrupted during the regular season, while employees were still at work, notice or compensation would be required.
Temporary layoff
Notice is also not required if an employee is laid off temporarily. A temporary layoff becomes a termination when a layoff exceeds 13 weeks in any period of 20 weeks, or a recall period covered by a collective agreement has been exceeded by more than 24 hours. A week of layoff is one in which the employee earns less than 50% of the regular weekly wages averaged over the previous eight weeks. If a temporary layoff becomes a termination, then the date of layoff becomes the termination date. The employee is entitled to the compensation for termination. Any layoff other than a temporary layoff is considered a termination.
Group terminations
When an employer intends to terminate 50 or more employees at a single location within a period of two months, the employer must provide written notice of group termination to each employee affected. The employer must also notify the Employment Standards Branch and any trade union that represents the employees. The length of notice depends on the number of employees to be laid off:
- 50 to 100 employees, at least eight weeks before the effective date of the first termination
- 101 to 300 employees, at least 12 weeks before the effective date of the first termination
- 301 or more, at least 16 weeks before the effective date of the first termination
Employers must give termination pay or a combination of termination pay and notice if the employees are not given the notice by the group termination requirements. If an employee is not covered by a collective agreement, the notice and termination pay requirements are in addition to the requirements based on length of employment.
If the employer is in receivership, bankruptcy, or insolvency, the provisions for group termination do not apply. However, the employee is still entitled to the amount which is payable as a result of length of employment, or the amount payable for an individual termination under the collective agreement, whichever is greater.
Employees covered by collective agreements
If an employee covered by a collective agreement that includes individual termination and right of recall provisions is laid off, the employee must choose to be paid the amount of compensation required by the collective agreement or to maintain his or her right of recall under the collective agreement. If the employee chooses to be paid, then the employer must pay that amount within 48 hours. If the employee chooses to maintain the right of recall or does not make a choice after 13 weeks of layoff, the employer must pay the amount required by the collective agreement to the Employment Standards Branch, in trust. Amounts received in trust receive interest and are paid to the employer if the employee is recalled.
If the employee renounces the right of recall or is not recalled to employment during the period required in the collective agreement, the amount held in trust is paid to the employee. Employees who accept employment under the right of recall do not have the right to payment of the money held in trust.
Other laws
Even in cases where no compensation or notice is required under the Employment Standards Act, other laws such as the Human Rights Code and common law regarding termination and wrongful dismissal may apply to a particular termination. Employers are required by federal government legislation to provide employees with a Record of Employment when they quit or are terminated. They must also issue a T-4 to employees who have income tax, Canada Pension, and Employment Insurance premiums deducted from their pay cheques whether or not they were working for the employer at the end of the year. The T-4 must be issued by February 28 of the following year.


9.9: Reactions of Acids and Bases
- Write acid-base neutralization reactions.
- Write reactions of acids with metals.
- Write reactions of bases with metals.
Neutralization Reactions
The reaction that happens when an acid, such as \(\ce{HCl}\), is mixed with a base, such as \(\ce{NaOH}\):
\[\ce{HCl (aq) + NaOH (aq) → NaCl (aq) + H_2O (l)}\nonumber \]
When an acid and a base are combined, water and a salt are the products.  Double displacement reactions of this type are called neutralization reactions . We can write an expanded version of this equation, with aqueous substances written in their longer form:
\[\ce{H^{+} (aq) + Cl^{-} (aq) + Na^{+} (aq) + OH^{-} (aq) → Na^{+} (aq) + Cl^{-} (aq) + H_2O (l)}\nonumber \]
After removing the spectator ions, we get the net ionic equation:
\[\ce{H^{+} (aq) + OH^{-} (aq) → H_2O (l)}\nonumber \]
When a strong acid and a strong base are combined in the proper amounts—when \([\ce{H^{+}}]\) equals \([\ce{OH^{-}}\)]\)—a neutral solution results in which pH = 7. The acid and base have neutralized each other, and the acidic and basic properties are no longer present.
Salt solutions do not always have a pH of 7, however. Through a process known as hydrolysis , the ions produced when an acid and base combine may react with the water molecules to produce a solution that is slightly acidic or basic. As a general concept, if a strong acid is mixed with a weak base, the resulting solution will be slightly acidic. If a strong base is mixed with a weak acid, the solution will be slightly basic.
Calcium propionate is used to inhibit the growth of molds in foods, tobacco, and some medicines. Write a balanced chemical equation for the reaction of aqueous propionic acid (CH 3 CH 2 CO 2 H) with aqueous calcium hydroxide [Ca(OH) 2 ].
Solution
| Steps | Reaction |
|---|---|
|
Write the unbalanced equation. This is a double displacement reaction, so the cations and anions swap to create the water and the salt. |
CH 3 CH 2 CO 2 H(aq) + Ca(OH) 2 (aq)→(CH 3 CH 2 CO 2 ) 2 Ca(aq) + H 2 O(l) |
|
Balance the equation. Because there are two OH − ions in the formula for Ca(OH) 2 , we need two moles of propionic acid, CH 3 CH 2 CO 2 H , to provide H + ions. |
2 CH 3 CH 2 CO 2 H(aq) + Ca(OH) 2 (aq)→(CH 3 CH 2 CO 2 ) 2 Ca(aq) + 2 H 2 O(l) |
Write a balanced chemical equation for the reaction of solid barium hydroxide with dilute acetic acid.
- Answer
-
\[\ce{Ba(OH)2(s) + 2CH3CO2H (aq)→Ba(CH3CO2)2 (aq) + 2H2O(l)} \nonumber \nonumber \]
Acids and Bases React with Metals
Acids react with most metals to form a salt and hydrogen gas. As discussed previously, metals that are more active than acids can undergo a single displacement reaction . For example, zinc metal reacts with hydrochloric acid, producing zinc chloride and hydrogen gas.
\[\ce{Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)}\nonumber \]
Bases also react with certain metals, like zinc or aluminum, to produce hydrogen gas. For example, sodium hydroxide reacts with zinc and water to form sodium zincate and hydrogen gas.
\[\ce{Zn(s) + 2NaOH (aq) + 2H2O(l) → Na2Zn(OH)4(aq) + H2 (g)}.\nonumber \]


11.1: The Interstellar Medium
Learning Objectives
By the end of this section, you will be able to:
- Explain how much interstellar matter there is in the Milky Way, and what its typical density is
- Describe how the interstellar medium is divided into gaseous and solid components
Astronomers refer to all the material between stars as interstellar matter; the entire collection of interstellar matter is called the interstellar medium (ISM) . Some interstellar material is concentrated into giant clouds, each of which is known as a nebula (plural “nebulae,” Latin for “clouds”). The best-known nebulae are the ones that we can see glowing or reflecting visible light; there are many pictures of these in this chapter.
Interstellar clouds do not last for the lifetime of the universe. Instead, they are like clouds on Earth, constantly shifting, merging with each other, growing, or dispersing. Some become dense and massive enough to collapse under their own gravity, forming new stars. When stars die, they, in turn, eject some of their material into interstellar space. This material can then form new clouds and begin the cycle over again.
About 99% of the material between the stars is in the form of a gas —that is, it consists of individual atoms or molecules. The most abundant elements in this gas are hydrogen and helium (which we saw are also the most abundant elements in the stars), but the gas also includes other elements. Some of the gas is in the form of molecules—combinations of atoms. The remaining 1% of the interstellar material is solid—frozen particles consisting of many atoms and molecules that are called interstellar grains or interstellar dust (Figure \(\PageIndex{1}\)). A typical dust grain consists of a core of rocklike material (silicates) or graphite surrounded by a mantle of ices; water, methane, and ammonia are probably the most abundant ices.
If all the interstellar gas within the Galaxy were spread out smoothly, there would be only about one atom of gas per cm 3 in interstellar space. (In contrast, the air in the room where you are reading this book has roughly 10^19 atoms per cm 3 .) The dust grains are even scarcer. A km 3 of space would contain only a few hundred to a few thousand tiny grains, each typically less than one ten-thousandth of a millimeter in diameter. These numbers are just averages, however, because the gas and dust are distributed in a patchy and irregular way, much as water vapor in Earth’s atmosphere is often concentrated into clouds.
In some interstellar clouds, the density of gas and dust may exceed the average by as much as a thousand times or more, but even this density is more nearly a vacuum than any we can make on Earth. To show what we mean, let’s imagine a vertical tube of air reaching from the ground to the top of Earth’s atmosphere with a cross-section of 1 square meter. Now let us extend the same-size tube from the top of the atmosphere all the way to the edge of the observable universe—over 10 billion light-years away. Long though it is, the second tube would still contain fewer atoms than the one in our planet’s atmosphere.
While the density of interstellar matter is very low, the volume of space in which such matter is found is huge, and so its total mass is substantial. To see why, we must bear in mind that stars occupy only a tiny fraction of the volume of the Milky Way Galaxy. For example, it takes light only about four seconds to travel a distance equal to the diameter of the Sun, but more than four years to travel from the Sun to the nearest star. Even though the spaces among the stars are sparsely populated, there’s a lot of space out there!
Astronomers estimate that the total mass of gas and dust in the Milky Way Galaxy is equal to about 15% of the mass contained in stars. This means that the mass of the interstellar matter in our Galaxy amounts to about 10 billion times the mass of the Sun. There is plenty of raw material in the Galaxy to make generations of new stars and planets (and perhaps even astronomy students).
Example \(\PageIndex{1}\): Estimating Interstellar Mass
You can make a rough estimate of how much interstellar mass our Galaxy contains and also how many new stars could be made from this interstellar matter. All you need to know is how big the Galaxy is and the average density using this formula:
\[ \text{total mass } = \text{ volume } \times \text{ density of atoms } \times \text{ mass per atom } \nonumber\]
You have to remember to use consistent units—such as meters and kilograms. We will assume that our Galaxy is shaped like a cylinder; the volume of a cylinder equals the area of its base times its height
\[V=\pi R^2h \nonumber\]
where \(R\) is the radius of the cylinder and \(h\) is its height.
Suppose that the average density of hydrogen gas in our Galaxy is one atom per cm 3 . Each hydrogen atom has a mass of 1.7 × 10 −27 kg. If the Galaxy is a cylinder with a diameter of 100,000 light-years and a height of 300 light-years, what is the mass of this gas? How many solar-mass stars (2.0 × 10 30 kg) could be produced from this mass of gas if it were all turned into stars?
- Answer
-
Recall that 1 light-year = 9.5 × 10 12 km = 9.5 × 10 17 cm, so the volume of the Galaxy is
\[ V= \pi R^2 h = \pi \left( 50,000 \times 9.5 \times 10^{17} \text{ cm} \right)^2 \left( 300 \times 9.5 \times 10^{17} \text{ cm} \right) = 2.0×10^{66} \text{ cm}^3 \nonumber\]
The total mass is therefore
\[M=V \times \text{ density of atoms } \times \text{ mass per atom} \nonumber\]
\[2.0 \times 10^{66} \text{ cm}^3 \times \left(1 \text{ atom/cm}^3 \right) \times 1.7 \times 10^{–27} \text{ kg} =3.5 \times 10^{39} \text{ kg} \nonumber\]
This is sufficient to make
\[N= \frac{M}{\left( 2.0 \times 10^{30} \text{ kg} \right)}=1.75 \times 10^9 \nonumber\]
stars equal in mass to the Sun. That’s roughly 2 billion stars.
Exercise \(\PageIndex{1}\)
You can use the same method to estimate the mass of interstellar gas around the Sun. The distance from the Sun to the nearest other star, Proxima Centauri, is 4.2 light-years. We will see in Interstellar Matter around the Sun that the gas in the immediate vicinity of the Sun is less dense than average, about 0.1 atoms per cm 3 . What is the total mass of interstellar hydrogen in a sphere centered on the Sun and extending out to Proxima Centauri? How does this compare to the mass of the Sun? It is helpful to remember that the volume of a sphere is related to its radius:
\[ V=(4/3) \pi R^3 \nonumber\]
- Answer
-
The volume of a sphere stretching from the Sun to Proxima Centauri is:
\[V=(4/3) \pi R^3=(4/3) \pi \left( 4.2 \times 9.5 \times 10^{17} \text{ cm} \right)^3=2.7×10^{56} \text{ cm}^3 \nonumber\]
Therefore, the mass of hydrogen in this sphere is:
\[M=V \times \left( 0.1 \text{ atom/cm}^3 \right) \times 1.7 \times 10^{–27} \text{ kg } = 4.5 \times 10^{28} \text{ kg} \nonumber\]
This is only \( \left(4.5 \times 10^{28} \text{ kg} \right)/ \left(2.0 \times 10^{30} \text{ kg} \right) = 2.2 /%\) the mass of the Sun.
NAMING THE NEBULAE
As you look at the captions for some of the spectacular photographs in this chapter and The Birth of Stars and the Discovery of Planets outside the Solar System, you will notice the variety of names given to the nebulae. A few, which in small telescopes look like something recognizable, are sometimes named after the creatures or objects they resemble. Examples include the Crab, Tarantula, and Keyhole Nebulae. But most have only numbers that are entries in a catalog of astronomical objects.
Perhaps the best-known catalog of nebulae (as well as star clusters and galaxies) was compiled by the French astronomer Charles Messier (1730–1817). Messier’s passion was discovering comets, and his devotion to this cause earned him the nickname “The Comet Ferret” from King Louis XV. When comets are first seen coming toward the Sun, they look like little fuzzy patches of light; in small telescopes, they are easy to confuse with nebulae or with groupings of many stars so far away that their light is all blended together. Time and again, Messier’s heart leapt as he thought he had discovered one of his treasured comets, only to find that he had “merely” observed a nebula or cluster.
In frustration, Messier set out to catalog the position and appearance of over 100 objects that could be mistaken for comets. For him, this list was merely a tool in the far more important work of comet hunting. He would be very surprised if he returned today to discover that no one recalls his comets anymore, but his catalog of “fuzzy things that are not comets” is still widely used. When Figure \(\PageIndex{1}\) refers to M4, it denotes the fourth entry in Messier’s list.
A far more extensive listing was compiled under the title of the New General Catalog ( NGC ) of Nebulae and Star Clusters in 1888 by John Dreyer, working at the observatory in Armagh, Ireland. He based his compilation on the work of William Herschel and his son John, plus many other observers who followed them. With the addition of two further listings (called the Index Catalogs ), Dreyer’s compilation eventually included 13,000 objects. Astronomers today still use his NGC numbers when referring to most nebulae and star groups.
Summary
About 15% of the visible matter in the Galaxy is in the form of gas and dust, serving as the raw material for new stars. About 99% of this interstellar matter is in the form of gas—individual atoms or molecules. The most abundant elements in the interstellar gas are hydrogen and helium. About 1% of the interstellar matter is in the form of solid interstellar dust grains.
Glossary
- interstellar dust
- tiny solid grains in interstellar space thought to consist of a core of rocklike material (silicates) or graphite surrounded by a mantle of ices; water, methane, and ammonia are probably the most abundant ices
- interstellar medium (ISM)
- (or interstellar matter) the gas and dust between the stars in a galaxy
- nebula
- a cloud of interstellar gas or dust; the term is most often used for clouds that are seen to glow with visible light or infrared
Contributors and Attributions
-
Andrew Fraknoi (Foothill College), David Morrison (NASA Ames Research Center), Sidney C. Wolff (National Optical Astronomy Observatory) with many contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/astronomy ).


9.7: Langmuir Circulation
One final type of wind-driven surface current occurs on a smaller scale when the winds blow in a consistent direction at relatively high speeds. Underneath these strong winds, water flows in a series of parallel corkscrew patterns called Langmuir cells (Figure \(\PageIndex{1}\) top). Each of the cells may be several meters wide and several meters deep, and adjacent cells rotate in opposite directions. While the overall direction of the corkscrew motion is in the direction of the wind, the rotation of the cells is roughly perpendicular to the wind direction. A divergence zone is created where the surface of the neighboring cells are rotating away from each other, and there is a degree of upwelling between the cells. Where the surface water of neighboring cells is rotating towards each other, a convergent zone is formed, with a region of downwelling between the cells. These alternating regions of divergence and convergence often take debris, foam, or algae floating at the surface and concentrate them along the convergence zones, creating long slicks running parallel to the wind direction (Figure \(\PageIndex{1}\) bottom).


5.5: Fractures - Bone Repair
By the end of this section, you will be able to:
- Differentiate among the different types of fractures
- Describe the steps involved in bone repair
A fracture is a broken bone. It will heal whether or not a physician resets it in its anatomical position. If the bone is not reset correctly, the healing process will keep the bone in its deformed position. When a broken bone is manipulated and set into its natural position without surgery, the procedure is called a closed reduction . Open reduction requires surgery to expose the fracture and reset the bone. While some fractures can be minor, others are quite severe and result in grave complications. For example, a fractured diaphysis of the femur has the potential to release fat globules into the bloodstream. These can become lodged in the capillary beds of the lungs, leading to respiratory distress and if not treated quickly, death.
Types of Fractures
Fractures are classified by their complexity, location, and other features (Figure \(\PageIndex{1}\)). Table \(\PageIndex{1}\) outlines common types of fractures. Some fractures may be described using more than one term because it may have the features of more than one type (e.g., an open transverse fracture).
| Type of fracture | Description |
|---|---|
| Transverse | Occurs straight across the long axis of the bone |
| Oblique | Occurs at an angle that is not 90 degrees |
| Spiral | Bone segments are pulled apart as a result of a twisting motion |
| Comminuted | Several breaks result in many small pieces between two large segments |
| Impacted | One fragment is driven into the other, usually as a result of compression |
| Greenstick | A partial fracture in which only one side of the bone is broken |
| Open (or compound) | A fracture in which at least one end of the broken bone tears through the skin; carries a high risk of infection |
| Closed (or simple) | A fracture in which the skin remains intact |
Bone Repair
When a bone breaks, blood flows from any vessel torn by the fracture. These vessels could be in the periosteum, osteons, and/or medullary cavity. The blood begins to clot, and about six to eight hours after the fracture, the clotting blood has formed a fracture hematoma (Figure \(\PageIndex{2.a}\)). The disruption of blood flow to the bone results in the death of bone cells around the fracture.
Within about 48 hours after the fracture, chondrocytes from the endosteum have created an internal callus (plural = calli) by secreting a fibrocartilaginous matrix between the two ends of the broken bone, while the periosteal chondrocytes and osteoblasts create an external callus of hyaline cartilage and bone, respectively, around the outside of the break (Figure \(\PageIndex{2.b}\)). This stabilizes the fracture.
Over the next several weeks, osteoclasts resorb the dead bone; osteogenic cells become active, divide, and differentiate into osteoblasts. The cartilage in the calli is replaced by trabecular bone via endochondral ossification (Figure \(\PageIndex{2.c}\)).
Eventually, the internal and external calli unite, compact bone replaces spongy bone at the outer margins of the fracture, and healing is complete. A slight swelling may remain on the outer surface of the bone, but quite often, that region undergoes remodeling (Figure \(\PageIndex{2}\).d), and no external evidence of the fracture remains.
Concept Review
Fractured bones may be repaired by closed reduction or open reduction. Fractures are classified by their complexity, location, and other features. Common types of fractures are transverse, oblique, spiral, comminuted, impacted, greenstick, open (or compound), and closed (or simple). Healing of fractures begins with the formation of a hematoma, followed by internal and external calli. Osteoclasts resorb dead bone, while osteoblasts create new bone that replaces the cartilage in the calli. The calli eventually unite, remodeling occurs, and healing is complete.
Review Questions
Q. A fracture can be both ________.
A. open and closed
B. open and transverse
C. transverse and greenstick
D. greenstick and comminuted
- Answer
-
Answer: B
Q. How can a fractured diaphysis release fat globules into the bloodstream?
A. The bone pierces fat stores in the skin.
B. The yellow marrow in the diaphysis is exposed and damaged.
C. The injury triggers the body to release fat from healthy bones.
D. The red marrow in the fractured bone releases fat to heal the fracture.
- Answer
-
Answer: B
Q. In a compound fracture, ________.
A. the break occurs at an angle to the bone
B. the broken bone does not tear the skin
C. one fragment of broken bone is compressed into the other
D. broken bone pierces the skin
- Answer
-
Answer: D
Q. The internal and external calli are replaced by ________.
A. hyaline cartilage
B. trabecular bone
C. osteogenic cells
D. osteoclasts
- Answer
-
Answer: B
Q. The first type of bone to form during fracture repair is ________ bone.
A. compact
B. lamellar
C. spongy
D. dense
- Answer
-
Answer: C
Critical Thinking Questions
Q. What is the difference between closed reduction and open reduction? In what type of fracture would closed reduction most likely occur? In what type of fracture would open reduction most likely occur?
- Answer
-
A. In closed reduction, the broken ends of a fractured bone can be reset without surgery. Open reduction requires surgery to return the broken ends of the bone to their correct anatomical position. A partial fracture would likely require closed reduction. A compound fracture would require open reduction.
Q. In terms of origin and composition, what are the differences between an internal callus and an external callus?
- Answer
-
A. The internal callus is produced by cells in the endosteum and is composed of a fibrocartilaginous matrix. The external callus is produced by cells in the periosteum and consists of hyaline cartilage and bone.
Glossary
- closed reduction
- manual manipulation of a broken bone to set it into its natural position without surgery
- external callus
- collar of hyaline cartilage and bone that forms around the outside of a fracture
- fracture
- broken bone
- fracture hematoma
- blood clot that forms at the site of a broken bone
- internal callus
- fibrocartilaginous matrix, in the endosteal region, between the two ends of a broken bone
- open reduction
- surgical exposure of a bone to reset a fracture
Contributors and Attributions
-
OpenStax Anatomy & Physiology (CC BY 4.0). Access for free at https://openstax.org/books/anatomy-and-physiology


8.1: Brahm’s Violin Concerto
Rather than having you read about this great violin concerto, I’d like you to listen to this discussion of the work on NPR . They spend some time talking about the particular recording that they are reviewing, but most of the discussion focuses on the work itself. There is one term that, while not mentioned in the recorded discussion, is very important to know when listening to this piece: double-stop . Double-stop is the term used when a violinist (or other bowed stringed instrumentn such as viola or cello) plays two strings at once instead of playing a single string which is the norm. You’ll hear extensive use of double stops in both the 1st and 3rd movements of this concerto (the 3rd is the only movement on our playlist).
Contributors and Attributions
- Authored by : Elliott Jones. Provided by : Santa Ana College. Located at : http://www.sac.edu . License : CC BY: Attribution


1.0: Introduction to Functions
Standard and Poor’s Index with dividends reinvested (credit "bull": modification of work by Prayitno Hadinata; credit "graph": modification of work by MeasuringWorth)
Toward the end of the twentieth century, the values of stocks of internet and technology companies rose dramatically. As a result, the Standard and Poor’s stock market average rose as well. The chart on the right tracks the value of that initial investment of just under $100 over the 40 years. It shows that an investment that was worth less than $500 until about 1995 skyrocketed up to about $1,100 by the beginning of 2000. That five-year period became known as the "dot-com bubble" because so many internet startups were formed. As bubbles tend to do, though, the dot-com bubble eventually burst. Many companies grew too fast and then suddenly went out of business. The result caused the sharp decline represented on the graph beginning at the end of 2000.
Notice, as we consider this example, that there is a definite relationship between the year and stock market average. For any year we choose, we can determine the corresponding value of the stock market average. In this chapter, we will explore these kinds of relationships and their properties.